Abstract
We prove that for any n≥2 there exists an ergodic measure-preserving transformation with homogeneous spectrum of multiplicity n in the orthogonal complement of the constant functions. This gives a complete solution of Rokhlin’s problem on homogeneous spectrum in ergodic theory. The transformations we provide belong to the class of finite rank transformations.
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Ageev, O. The homogeneous spectrum problem in ergodic theory. Invent. math. 160, 417–446 (2005). https://doi.org/10.1007/s00222-004-0422-z
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DOI: https://doi.org/10.1007/s00222-004-0422-z